(207g) Learning-Based Data Reconstruction and Predictive Modeling of an Ammonia Synthesis Process for State Estimation and Control Applications

Ammonia is essential for producing fertilizers and is the second most-generated synthetic chemical worldwide [1, 2]. In addition, ammonia is used as a refrigerant gas, to produce plastics, explosives, pesticides, textiles, dyes, and has recently been considered a promising carbon-free hydrogen carrier for energy storage and transportation [3-5]. The industrial-scale production of ammonia is via thermochemical synthesis with the well-known Haber-Bosch process [6]. Nitrogen and hydrogen are mixed on the surface of a metal-based catalyst in a high-pressure, high-temperature reactor to produce ammonia [7]. Controlling the functioning of such a reactor requires precise descriptions of the reaction mechanism, as well as control methods that drive reactions into lower energy and more selective paths.

The first step toward controlling ammonia synthesis is to develop a reliable model that predicts the reactor's complex nonlinear dynamics. Reaction rates computed at smaller length scales are only applicable over a specific discretization size due to the much larger gradients in momentum, energy, and mass transport fields at the macroscopic reactor scale compared to the spatial heterogeneity of catalyst properties at the microscale. To account for temperature and species concentration variations, rates must be re-evaluated at various macroscopic domains. Integrating transport-reaction spatiotemporal dynamics across the process domain then determines macroscopic behavior. Hence, only a multiscale model that links microscopic features to macroscopic process variables that can be monitored and changed can predict such intimate events. A multiscale interpretation of transport-catalytic ammonia synthesis requires high-fidelity and computationally tractable fundamental models that can reliably anticipate the system's spatiotemporal dynamics, allowing information transmission across scales.

In this work, we employ a high-fidelity multiscale model of catalytic ammonia synthesis in an industrial-scale packed-bed reactor. Integrating ammonia reaction kinetics [7, 8] with a comprehensive transport model of the reactor results in a set of nonlinear algebraic and partial differential equations that must be solved simultaneously to predict the spatiotemporal dynamics of the pressure, temperature, and species concentrations. The multiscale model increases ammonia synthesis understanding and prediction accuracy. However, its complexity and computational inefficiency limit its use for real-time simulation, analysis, and model-based estimation and control approaches such as model predictive control (MPC) and moving horizon estimation (MHE). In MPC and MHE, the control and estimation problems are formulated as constrained dynamic optimization problems that must be solved repeatedly at each process sampling time to get the current values of the manipulated inputs and estimating the unmeasured state variables [9]. Hence, the applicability of MPC and MHE relies on the real-time solvability of the underlying dynamic optimization problem subject to the process model and constraints.

The computational intensity of the proposed high-fidelity multiscale model makes it incompatible with optimization-based state estimation and control. Therefore, a Long-Short Term Memory (LSTM)-based reduced-order model is used to approximate the dynamic behavior described by the high-fidelity model. COMCOL Multiphysics is used to run offline high-fidelity simulations under different operating conditions to get the data needed to build the reduced-order model. This non-uniform resolution of the simulation data and the complexity of the solution trends cause bimodality behavior in the training dataset, which may lead to inconsistently trained reduced-order models, making the LSTM network be trained only based on the dominant mode and ignoring the rest of the nonlinear patterns. We apply a feedforward neural network (FNN) to address the bimodality problem by increasing the resolution of the offline simulated data. The offline simulated data is used to train the FNN and reconstruct the dataset at a higher resolution, leading to a normal distribution. Furthermore, the reconstructed dataset is used to train the LSTM network in a multivariate time-series forecast manner. The reduced-order model is examined and utilized as the basis for the MPC and MHE designs. The resulting closed-loop performance in regulating the reactor's temperature and concentration is evaluated under various operating conditions.

References:

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